Answer:
Below are explanations!
Step-by-step explanation:
6) 5^4/5^2 means the ^4 and ^2 needs to subtract from the 5s. This results in 5^2, which equals 25.
7) The 9 as the denominator will cross with the first nine above. This leaves as follows: 9^3 x 9^2 x 9^6 (I don't know if it is a 6 or 0). You may solve from there. Just add all the exponents up.
8)^-6 will be multiplied by ^6, which is ^-36. Therefore, the answer is 5^-36.
The other questions, please, remember to read carefully.
The slope is 100. It represents the cost per wristband.
The y-intercept is 1500. It represents the fixed cost to manufacture the wristbands.
<span>It will take 20 minutes. The fridge needs to cool down by 90-50=40degrees. The fridge cools at 2 degrees per minute, i.e. 40/2=20 minutes total.</span>
Search it up on the internet But this is how far my calculater goes. 94.1224489796
Answer:
Step-by-step explanation:
<h3>Polynomial:</h3>
p(x) = ax³ + bx + x
Let g(x) = x² + kx + 1 .
g(x) is a factor of p(x). So, p(x) is divided by g(x), the remainder will be 0.
Divide p(x) by g(x) using long division method. {attached as an image}.
By doing long division, we get the remainder.
Remainder = bx - ax + k²ax + ka + c
= (b - a + k²a)x+ [ka + c]
Remainder = 0
b - a + k²a = 0 and ka + c = 0
ka + c = 0
ka = -c
k = -c/a ----------------(I)
b - a + k²a = 0
![\sf b -a + \dfrac{c^2}{a^2}*a=0 -------[From \ (I)]\\\\b - a + \dfrac{c^2}{a}=0\\\\Multiply \ the \ above \ equation\ by \ a \\\\ab - a^2 + c^2 = 0\\\\\\](https://tex.z-dn.net/?f=%5Csf%20b%20-a%20%2B%20%5Cdfrac%7Bc%5E2%7D%7Ba%5E2%7D%2Aa%3D0%20%20%20-------%5BFrom%20%5C%20%28I%29%5D%5C%5C%5C%5Cb%20-%20a%20%20%2B%20%5Cdfrac%7Bc%5E2%7D%7Ba%7D%3D0%5C%5C%5C%5CMultiply%20%5C%20the%20%5C%20above%20%5C%20equation%5C%20by%20%5C%20a%20%5C%5C%5C%5Cab%20-%20a%5E2%20%2B%20c%5E2%20%3D%200%5C%5C%5C%5C%5C%5C)
ab = a² - c²
Hence, proved.
